The deposition of ultrathin Fe films on the Mo(110) surface at elevated temperatures results in the formation of distinctive nanowedge islands supported on a pseudomorphic Fe layer. We propose a model explaining the growth mode of these wedge-shaped Fe islands. The model is based on the strain produced in the substrate around each island, by the lattice mismatch between the film and substrate. Fe adatoms migrate towards the islands due to the influence of this strain, which is related to the thickness and size of each island. The adatoms subsequently enter the islands not only through their thin ends where the island can be only two monolayers thick but on the contrary, through a vertical climb along the sides of the thicker end, which can be tens of layers thick. This mode of mass transport is again driven by strain, corresponding to the energy reduction through movement towards the location where the interatomic spacing in the island corresponds to the bulk value. A key element of the model is that misfit dislocations are formed in the lower layers of the nanowedge, which act as migration channels for the vertical climb.